PHOEG Helps to Obtain Extremal Graphsch:32

Gauvain Devillez, Pierre Hauweele () and Hadrien Mélot
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Gauvain Devillez: University of Mons
Pierre Hauweele: University of Mons
Hadrien Mélot: University of Mons

A chapter in Operations Research Proceedings 2018, 2019, pp 251-257 from Springer

Abstract: Abstract We present PHOEG, an ecosystem of tools designed to help researchers in Extremal Graph Theory. It uses a big relational database of undirected graphs and works with the convex hull of the graphs as points in the invariants space in order to exactly obtain the extremal graphs and optimal bounds on the invariants for some fixed parameters. The results obtained on the restricted finite class of graphs can later be used to infer conjectures. This database also allows us to make queries on those graphs. Once the conjecture defined, PHOEG goes one step further by helping in the process of designing a proof guided by successive applications of transformations from any graph to an extremal graph. To this aim, we use a second database based on a graph data model.

Date: 2019
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DOI: 10.1007/978-3-030-18500-8_32

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